Elastic
potential energy
Elastic
potential energy
Yippee!!
Objectives
•
Investigate examples of elastic potential energy.
•
Provide or identify a conceptual definition of the spring
constant.
•
Calculate the potential energy, spring constant, or
deflection of a spring using the elastic potential energy
equation.
Preliminary Questions
1. What do each of the symbols mean in
the equation PEelastic = ½ kx2?
2. Translate the equation EP = ½ kx2 into
a sentence with the same meaning.
3. How much elastic potential energy is
stored in a 100 N/m spring that is
compressed 0.10 meters?
4. A spring has an elastic potential
energy of 100 J when compressed
0.10 m. What is its spring constant?
5. How far is a spring extended if it has
1.0 J of elastic potential energy and
its spring constant is 1,000 N/m?
6. Are these statements about the
spring constant true or false?
a) ___ The spring constant is a
measure of the stiffness of the
spring.
b) ___ The spring constant tells you
how many newtons of force it
takes to stretch the spring one
meter.
c) ___ If a spring stretches easily, it
will have a high spring constant.
d) ___ The spring constant of a spring
varies with x, the amount of
stretch or compression of the
spring.
Physics terms
•
elastic potential energy
•
spring constant
Equations
The elastic potential energy of a spring is one half the product
of its spring constant multiplied by the square of its extension
or compression.
Work and energy
Energy may be stored in a
system when work is done on
the system.
Springs
Force and deformation
When you apply a force to a spring, it deforms.
Work
The force applied does work on the spring.
The change in the spring’s length is called the deformation, x.
Review – free length
The free length is the length of the spring without any external
forces applied.
Elastic potential energy
The work is stored in the spring as elastic potential energy.
Force
The force from a spring
starts at zero and
increases.
Force
The force from a spring
starts at zero and
increases. The work
against this force gets
stored as Ep.
Equations
The elastic potential energy of a
spring is one half the product of its
spring constant multiplied by the
square of its deformation.
What is the spring constant, k?
The spring constant of a spring tells us its stiffness.
•Stiff springs have high spring constants
•Weak springs have low spring constants.
The spring constant, k, doesn’t change when the spring
is compressed or stretched.
Units of the spring constant
•
The spring constant has units of N/m, or newtons per meter.
•
Example: A 300 N/m spring requires 300 N of force to
stretch 1 meter.
•
A stiff spring needs a large force to stretch it one meter, so
it has a large spring constant.
Calculating force (Hooke’s law)
Fapplied
+
Calculating force (Hooke’s law)
Fspring
Fapplied
+
Calculating force (Hooke’s law)
Fspring
Fapplied
+
Fs is the restoring
force exerted by the
spring. It is always
directed opposite the
displacement.
Calculating force (Hooke’s law)
Fspring
Fapplied
+
Fs is the restoring
force exerted by the
spring. It is always
directed opposite the
displacement.
Fs = kx
Fs = (20, 000 N/m)( 0.01 m)
Fs = 200 N
Calculating force (Hooke’s law)
Fspring
Fapplied
+
Fs is the restoring
force exerted by the
spring. It is always
directed opposite the
displacement.
Fs = kx
Fs = (20, 000 N/m)( 0.01 m)
Fs = 200 N (45 lbs)
Calculating force (Hooke’s law)
Fspring
Fapplied
+
1 cm
Fs is the restoring
force exerted by the
spring. It is always
directed opposite the
displacement.
Fs = kx
Fs = (20, 000 N/m)( 0.01 m)
Fs = 200 N (45 lbs)
Perfect for a mountain bike fork!
A spring is inside the
fork tube.
Engaging with the concepts
How much work must be done to
compress a k = 1.0 N/m spring by
25 cm?
Engaging with the concepts
How much work must be done to
compress a k = 1.0 N/m spring by
25 cm?
0.03 J
Engaging with the concepts
How about a k = 100 N/m spring?
Engaging with the concepts
How about a k = 100 N/m spring?
3.1 joules
Engaging with the concepts
How does the stored energy
change if the spring is compressed
by 10 cm versus being extended by
10 cm?
Engaging with the concepts
How does the stored energy
change if the spring is compressed
by 10 cm versus being extended by
10 cm?
The elastic potential energy is the
same—try other positive and
negative values!
Engaging with the concepts
How does the stored energy change
if the spring constant is doubled?
Engaging with the concepts
How does the stored energy change
if the spring constant is doubled?
The energy doubles.
Engaging with the concepts
How about if the spring is
compressed by twice as much?
Engaging with the concepts
How about if the spring is
compressed by twice as much?
The energy increases by a factor
of four (22).
Elastic potential energy
Where does this formula come from?
Is it a fundamental law of physics?
Elastic potential energy
Where does this formula come from?
Is it a fundamental law of physics? No!
Elastic potential energy
This represents the work done to
deform the spring by an amount x.
Work
W = Fd
Work is force times distance.
Work
W = Fd
Hypothesis: The elastic potential
energy is the work done to deform
the spring from its free length.
Work
W = Fd
Hypothesis: The elastic potential
energy is the work done to deform
the spring from its free length by a
distance x.
Hooke’s law
W = Fd
F = kx
Hooke’s law
W = Fd
F = kx
where x is the change in length of
the spring.
Hooke’s law
W = Fd
F = kx
where x is the change in length of
the spring.
and k is the spring constant in N/m.
Force vs. Distance
On a graph of force vs. distance ...
Force vs. Distance
On a graph of force vs. distance
this is a straight line.
Force vs. Distance
The area on this graph ...
Force vs. Distance
The area on this graph is force times
distance ...
Force vs. Distance
The area on this graph is force times
distance which is the work done!
Force vs. Distance
Force vs. Distance
Force vs. Distance
Force vs. Distance
Elastic potential energy
The elastic potential energy is equal to the work done to
convert the spring from its free length into its deflected length.
Elastic potential energy
This is true for more than just springs!
Elastic potential energy
Elastic potential energy is stored in all objects that can deform
and spring back to their original shape.
Elastic potential energy
such as a rubber band ...